On Large N Solution of N=3 Chern-Simons-adjoint Theories

Takao Suyama

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On Large N Solution of N=3 Chern-Simons-adjoint Theories

Takao Suyama

High Energy Physics - Theory · Submitted 10 Aug 2012

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim The vev of a Wilson loop does not exhibit an exponential growth although such a behavior would be expected for theories with classical gravity duals.

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The planar resolvent for N=3 U(N)_k Chern-Simons theory coupled to an arbitrary number of adjoint matters is determined. Analytic continuation of the 't Hooft coupling t is analyzed. The eigenvalue distribution turns out to be confined in a finite region even for a large t. The vev of a Wilson loop does not exhibit an exponential growth although such a behavior would be expected for theories with classical gravity duals.

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#	sentence	role	the authors' own work	states the main conclusion	strength
s0	The planar resolvent for N=3 U(N)_k Chern-Simons theory coupled to an arbitrary number of adjoint matters is determined.	contribution 0.57	0.90	0.39	asserted 1.00
s1	Analytic continuation of the 't Hooft coupling t is analyzed.	contribution 0.72	0.85	0.05	asserted 0.82
s2	The eigenvalue distribution turns out to be confined in a finite region even for a large t.	result 1.00	0.92	0.27	asserted 1.00
s3	The vev of a Wilson loop does not exhibit an exponential growth although such a behavior would be expected for theories with classical gravity duals.	result 0.88	0.83	0.36	asserted 1.00

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The paper

Original abstract

The planar resolvent for N=3 U(N)_k Chern-Simons theory coupled to an arbitrary number of adjoint matters is determined. Analytic continuation of the 't Hooft coupling t is analyzed. The eigenvalue distribution turns out to be confined in a finite region even for a large t. The vev of a Wilson loop does not exhibit an exponential growth although such a behavior would be expected for theories with classical gravity duals.

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References

Forward citations

Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

Exact results on ABJ theory and the refined topological string
hep-th 2014-05 conditional novelty 6.0 of 10

The ABJ partition function on the three-sphere is fixed, order by order in instantons, by the refined topological string on local P1 x P1, extending the ABJM correspondence to nonzero fractional brane number M.
M-theoretic matrix models
hep-th 2014-03 conditional novelty 6.0 of 10

Two matrix models relevant to M-theory and 2d statistical physics are solved exactly in the planar limit, and their M-theory expansions reveal non-perturbative corrections invisible to the 't Hooft expansion.
Partition Functions of Superconformal Chern-Simons Theories from Fermi Gas Approach
hep-th 2014-07 accept novelty 5.0 of 10

For general N=4 circular-quiver Chern-Simons theories the partition function takes the ABJM Airy form, with an explicit B, a conjectured A for separated quivers, and instanton divergences that cancel in the (2,1) model.

How the literature uses it

11 arXiv papers cite this in 40 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 25 sentences without a confident label

Builds on it 2 papers

To clarify the situation, it is desired to extend the analysis in [ref] to more general theories.

A Systematic Study on Matrix Models for Chern-Simons-matter Theories · Introduction · 0.93
Our case ([ref]) is recovered by simply setting $ξ=-1$, and one finds from [ref]

M-theoretic matrix models · The planar solution · 0.91

Uses its method or tool 3 papers

It was found in [ref] that the following ansatz [equation] for the resolvents is quite useful to deal with the logarithmic functions.

A Systematic Study on Matrix Models for Chern-Simons-matter Theories · Integral ansatz · 0.96
We follow the argument of the resolvent in [ref] .

Aspects of Massive Gauge Theories on Three Sphere in Infinite Mass Limit · A brief summary of resolvent methods · 0.99
It turns out that this model can be mapped to an $O(2)$ matrix model [ref] and studied with the techniques of [ref] (similarly to what was done in [ref] ).

Localization at large N in Chern-Simons-matter theories · The 't Hooft expansion of Chern–Simons–matter theories · 0.98

Compares with it 2 papers

These theories are rather similar to the Chern-Simons-adjoint theories investigated in [ref] .

A Systematic Study on Matrix Models for Chern-Simons-matter Theories · Discussion · 0.96
This solution differs from the one given in [ref] by an overall sign, and follows the conventions in [ref] .

M-theoretic matrix models · General properties · 0.99

Cites it as background 5 papers

In this section, we discuss the planar free energy of $N=3$ Chern-Simons-adjoint theories [ref] which may couple to fundamental matters.

Supersymmetry Breaking and Planar Free Energy in Chern-Simons-matter Theories · Planar free energy and resolvent · 0.90
In [ref] , $N=3$ Chern-Simons-adjoint theories were discussed.

A Systematic Study on Matrix Models for Chern-Simons-matter Theories · Chern-Simons-adjoint theory revisited · 0.95
However, if we consider more general M2-brane theory beyond[ For previous studies, see e.g. [ref] in the M-theory limit, [ref] in the 't Hooft limit and [ref] in the Fermi gas approach. ] the ABJ(M) theory, the correspondence to the topological string is rather obscure, and it might be the case that there is no such relation in general.

Exact results on ABJ theory and the refined topological string · Discussions · 0.94

What it cites · 34 sentences without a confident label

Uses the method or tool of 2 papers

A simpler technique was introduced in [ref] (see also [ref] for earlier discussion) which could extract the leading behavior of the free energy and the vev of BPS Wilson loops in the large $N$ limit.

On Large N Solution of ABJM Theory · Introduction · 0.87
A simpler technique was introduced in [ref] (see also [ref] for earlier discussion) which could extract the leading behavior of the free energy and the vev of BPS Wilson loops in the large $N$ limit.

Multi-Matrix Models and Tri-Sasaki Einstein Spaces · Introduction · 0.87

Compares with 2 papers

The singularity at $n=1$ seems to be compatible with the results in [ref] .

Eigenvalue Distributions in Matrix Models for Chern-Simons-matter Theories · Analytic continuation · 0.93
The eigenvalue distribution obtained from the resolvent has a similar property observed in [ref] .

Interacting fermions and N=2 Chern-Simons-matter theories · Introduction · 1.00

Cites as background 9 papers

The analysis for ABJM theory [ref] was performed and the planar resolvent was obtained explicitly in [ref] .

Exact Results in ABJM Theory from Topological Strings · Introduction · 0.81
The analysis for ABJM theory [ref] was performed and the planar resolvent was obtained explicitly in [ref] .

N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals · Introduction · 0.81
On the other hand, the traditional analysis of the saddle-point equations in terms of the resolvent has been developed in [ref] [ref] [ref] , but the range of applicability has been rather limited.

Eigenvalue Distributions in Matrix Models for Chern-Simons-matter Theories · Introduction · 0.91

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